Interpreting and Extending the Maximum Ratio Test of Unacceptability

Tsao and Wright (1983) proposes the use of a statistic called the “maximum ratio” to assess the reliability of K estimates of an unknown population parameter θ. This statistic can be used to test whether one of these estimates is outside of an “acceptable” region, whose radius is a multiple α of the unknown true parameter θ. Because θ is unknown, it is difficult to know whether a large α value reflects a large error in the underlying metric, or just a large proportion of a small θ. This paper generalizes the maximum ratio test to multiple dimensions, considers some broad approaches for selecting an α value for this test in the absence of knowledge of θ, applies the testto five estimates of the population proportions for eight demographic subgroups within the United States, and visualizes the results. We then repeat the process after intentionally introducing errors into one of the estimates. This paper is abridged from Hall (2024).